Question

Two particles of masses `m_(1),m_(2)` move with initial velocities `u_(1)` and `u_(2)`. On collision, one of the particles get excited to higher level, after absording enegry. If final velocities of particles be `v_(1)` and `v_(2)` then we must have
A. `(1)/(2) m_(1) u_(1)^(2) + (1)/(2) m_(2) u_(2)^(2) = (1)/(2) m_(1) v_(1)^(2) + (1)/(2) m_(2) v_(2)^(2) - epsilon`
B. `(1)/(2) m_(1) u_(1)^(2) + (1)/(2) m_(2) u_(2)^(2) epsilon = (1)/(2) m_(1) v_(1)^(2) + (1)/(2) m_(2) v_(2)^(2) `
C. `(1)/(2) m_(1)^(2) u_(1)^(2) + (1)/(2) m_(2)^(2) u_(2)^(2) epsilon = (1)/(2) m_(1)^(2) v_(1)^(2) + (1)/(2) m_(2)^(2) v_(2)^(2)`
D. `m_(1)^(2) + m_(2)^(2) u_(2) - epsilon = m_(1)^(2) v_(1) + m_(2)^(2) v_(2)`

Answer 1

The energy `in` comes initial kinetic energy
`K_(i) = (1)/(2) m_(1) u_(1)^(2) + (1)/(2) m_(2)u_(2)^(2)`
`K_(f) = (1)/(2) m_(1) v_(1)^(2) + (1)/(2) m_(1) v_(1)^(2) + in`
`K=_(i) = K_(f)`
`(1)/(2) m_(1) u_(1)^(2) + (1)/(2) m_(2) u_(2)^(2) - in = (1)/(2) m_(1) v_(2)^(2) + (1)/(2) m_(2) v_(2)^(2)`